The Manchester United forward was part of the teams that were beaten by both Italy and Uruguay in the opening two matches in Group D.
Those losses eventually saw the Three Lions eliminated from the tournament after Costa Rica defeated Italy on Friday.
It is the first time England have failed to qualify from the group stage of the tournament since 1958.
Rooney took to his official Facebook page to say sorry to the England supporters, writing:
Absolutely devastated to be out of the World Cup.
Going into each game we had great belief in ourselves but unfortunately it hasn't worked out.
Sorry to all the fans that travelled and at home that we haven't done better...gutted!
Rooney scored his first goal in a World Cup finals when he equalised against Uruguay in Sao Paulo.
However, two goals from Liverpool striker Luis Suarez were enough to down the Three Lions before Costa Rica's surprise win over the Azzurri confirmed their departure from Brazil before the knockout stages.
Rooney also received support from Manchester United team-mate Robin van Persie, as BBC Sport reported.
The Netherlands striker is quoted as saying:
I don't think you can blame him for scoring a goal, working his socks off and missing three chances by inches.
Wayne is a great player and part of why I came to Manchester United.
If you look at his performances, the things I've seen and heard were very good.
He played as a left winger, gave the assist for the 1-1 against Italy and played well as far as I know.